1. Philip Bucksbaum Stanford PULSE Center
Chapter 2 Control of Electrons and Nuclei in Atoms, Molecules, and Materials
Philip Bucksbaum
Stanford PULSE Center

2. Fundamental science challenges: Coherence and Control
Chapter 2 describes the challenge of understanding and controlling coherence in new ways.
Main concepts: Coherence and Control
Quantum coherence in materials control new phenomena
Quantum degeneracy and quantum coherence
Quantum coherence in photochemistry
Quantum coherence and information science
Coherence properties of novel light sources to control new materials
Chemical composition and chemical bond control
Laser-driven materials properties
Imaging materials in important new ways

3. We know there can be strong connections between materials and quantum coherence
Superconductivity is just one of a number of phases related to quantum coherence of electrons at low temperatures in certain materials.
Sophisticated magnetic materials are used widely (information storage, nanoscale sensors, and in the future for spintronics

4. The quantum state of matter at low temperatures: Quantum simulators
Vortex arrays in superfluids made of atoms, molecules, and BCS pairs (Ketterle, MIT)
Challenges: Quantum spin liquid at T  0: A triangular antiferromagnetic spin lattice (Physics Today, February 2007)
The future: simulating Quantum Chromodynamics? ((F. Wilczek, Nat. Phys 3, 375 (2007).)
New theoretical approaches beyond DFT and DMFT are needed .
Experimental control over cold atoms has now been used to demonstrate many exotic quantum properties: superfluidity, superconductivity, Bose-Einstein condensation, BCS pairing, etc

5. Excited state chemistry requires a new description
Avoided crossings of “spaghetti” of states of diatomics becomes a puff pastry of conical intersections in polyatomic molecules.
H2O anion - D. Haxton
NH3
Separation of timescales is the basis for theoretical approximations that simplify the calculation of molecular properties and dynamics, and provide a conceptual basis for understanding the fundamental physics.
when these approximations break down there is a great challenge for new approaches valid in these new regimes.
the Born- Oppenheimer approximation breaks down when the potential energy surfaces of two different electronic states of the molecule have the same energy for some geometry. Then very small changes in the geometry of the molecule can produce large changes in the motion of the electrons as the molecule flips between states.
In polyatomic molecules, the intersection of multidimensional potential energy surfaces play a critical role in how energy is redistributed among the electronic and vibrational motions of the molecule and, ultimately, in how the molecule reacts or decomposes.
Keys to photochemistry and photocatalysis
The molecular dynamics of combustion is significantly affected by the presence of molecules in electronically excited states.
Calculations of the structure and dynamics of molecules in electronically highly excited states remain extremely challenging.
These calculations are likely to entail a shift from frequency-domain to time-domain.
H3+ - C. H. Greene
“The Born-Oppenheimer approximation may be irrelevant. We don’t yet have a language to describe the physics these experiments can probe” -- W. Kohn

6. Why we can’t just calculate this stuff…
Moore’s original graph predicting Moore’s Law in Chip capacity will double every two years. This must fail soon (2007). Too bad for us, because we need much more computing power:
Kohn’s law: “Traditional multiparticle wave-function methods when applied to systems of many particles encounter an exponential wall when the number of atoms N exceeds a critical value which currently is in the neighborhood of N~10 (to within a factor of about 2)” (W. Kohn, Nobel Prize Address, 1999)
Figures:
Left: Visualization on the cover of Science of three of the hundreds of possible components of the quantum wave function for a two-electron system broken by collision with an electron. Right: Two of the many components of the quantum wave function for two electrons being ejected from the H2 molecule by a single photon.

7. Quantum simulators, or some other new computing paradigm, is required
Analog logic? 17nm features on a crossbar circuit, showing atomic-scale bumpiness. Analog circuit elements like memristors may be able to use such circuits more effectively.
Quantum computing?
(Quantum entanglement as a resource.)
An atomic force microscope topograph of a crossbar circuit fabricated by imprint lithography at a feature size (half-pitch) of 17 nm. The atomic scale granularity of matter is evident in this image because of the ‘bumpiness’ of the surfaces. Also, at this scale, various types of defects are obvious in the image – e.g. broken wires and filled-in gaps between wires. At some scale, it will no longer be economically sensible to build such structures perfectly.

8. Intense coherent sub-picosecond x-ray light sources will be able to track matter at extremes
• MD simulation of FCC copper
Periodic features  average distance between faults
Diffuse scattering from stacking fault
The physics of the transition from cold solid matter to hot plasma – through a regime often referred to as “warm dense matter” - is poorly understood, difficult to experimentally measure, and nearly impossible to calculate.
Yet this transition region occurs in systems ranging from white dwarfs and giant planets to plasma torches and inertial confinement fusion targets.
It holds promise of new phenomena, including finite-temperature analogs of quantum critical behavior, plasmas consisting of both positive and negative ions, and “black glass.”
It bridges a regime where atoms and ions dominate energy content, to one dominated by electrons, and is associated with an exponential explosion in the number of thermally accessible states.
In real systems, the transition is very fast, and non-equilibrium. The approach to the plasma state can, depending on the path, display anomalous properties and new structure determined by the interplay between the physics of isolated atoms and ions on the one hand, and the spatial correlations of condensed matter on the other.
Peak diffraction moves from 0,0 due to relaxation of lattice under pressure
S. K. Saxena & L. S. Dubrovinsky, American Mineralogist 85, 372 (2000).
J. C. Boettger & D. C. Wallace, Physical Review B 55, 2840 (1997).
C. S. Yoo et al., Physical Review Letters 70, 3931 (1993).
• X-ray diffraction image using LCLS probe of the (002) shows in situ stacking fault information

9. Coherent Control
The control of quantum phenomena takes engineering control principles into the realm of quantum mechanics
Time scales are picoseconds to attoseconds, and the size of objects under direct control are Angstroms to nanometers.
The intellectual pay-off of this field is vast: essentially all dynamics events start with the atomic and molecular scale, including all of chemistry, and much of materials science.
Lasers can now produce coherent radiation with almost any field strength, frequency, temporal shape, bandwidth, polarization. Coherent matter waves have been produced and manipulated in laboratories. Coherent quantum state engineering and control have become a reality. This will open new scientific directions.
A very exciting and challenging outlook is to incorporate the important aspect of coherent interactions between matter and field at these progressively higher energy scales. Such capabilities would allow detailed studies of matter structure at ever increasing spatial, time, and energy resolutions. Quantum dynamics and control will be realized at high energies. It would also enable controlled generations of beams of matter that are well characterized in energy, timing, and spatial location. A far-reaching vision would call for a unified “wave synthesizer” that connects electromagnetic radiations spanning 10 orders of magnitude in frequency scale with matter waves, in a phase coherent manner

10. COHERENT CONTROL IN MOLECULAR SYSTEMS
Pulse Shaping: the optimal field discovered by OCT often has a broad bandwidth, with its phases adjusted to give a highly structured pulse.
Learning Control: The learning loop brings the same feedback used in optimal control algorithms into the laboratory.

11. 1. Discover the general principles for control
Connections to nature: photosynthesis Electron motion drives nuclear motion
The retinal molecule (light blue) in the center of rhodopsin bends after absorbin light, to help move a proton across a membrane. Coherence enhancement?
Some molecules appears to utilize quantum coherence in the process of photosynthesis.
Challenges:
1. Discover the general principles for control
2. Real-time feedback for quantum control

12. New Experiments are showing us attosecond electron dynamics for the first time
The motion of electrons in atoms is femtoseconds or less.
If we had at our disposal short enough pulses to strobe the motion of electrons in chemistry and materials science, we could observe electron motion directly, which could lead to fundamental advances in these areas.
Fundamental science that can advance with attosecond resolution:
Non-radiative chemistry
Electronic coherence in atoms and molecules
Physics of inner electronic shells

13. QUANTUM ELECTRON SCATTERING
Figure: Collecting an image of a nitrogen molecule as it undergoes strong-field ionization and recollision (cartoon at left). The image collected from the radiation produced in the recollision is shown at the top right, and a calculation of the most loosely bound ground state electron in nitrogen is shown on the bottom right. (from AMO2010: Controlling the Quantum World. Original artwork from: D. Villeneuve, NRC, Ottawa.

14. X-ray laser science
Figure 13: The LCLS, Linac Coherent Light Source, when it is completed in 2009 at Stanford University, will be one-billion times brighter than currently existing synchrotrons.

15. Imaging with XFEL’s
XFEL light will be a billion times more brilliant than current sources, in bursts shorter than the movement of the atoms in a molecule.
Fundamental mechanisms of damage at such high intensities are not well understood.
Can the coherence of the x-ray laser change the character of the damage?

16. Questions that frame the challenges in this chapter:
A. Materials and coherence
1. How does electronic quantum coherence affect the properties of materials?
2. What is the role of quantum coherence in dynamics, especially photo-chemistry?
B. Coherence and control
1. How can we control the quantum states of matter by applying coherent fields? (Coherent control)
2. How does matter behave on the timescale of electron motion? (Attoscience)
3. How can we utilize new generations of coherent sources for materials science and chemical science?
Relevant time scales are 1e-18 to 1e-15 seconds.